# Questions tagged [formula-derivation]

The tag has no usage guidance.

87 questions
Filter by
Sorted by
Tagged with
3answers
6k views

### Why is inductance (L) proportional with turns-square (N²)?

We start from the Maxwell's Equation $$\mathbf{\nabla} \times \mathbf{B} = \mu \mathbf{J} + \overbrace{\mu \epsilon \dfrac{\partial \mathbf{E}}{\partial t}}^0.$$ We take surface integration of ...
2answers
25k views

### Deriving the formula from 'scratch' for charging a capacitor

So the formula for charging a capacitor is: $$v_c(t) = V_s(1 - exp^{(-t/\tau)})$$ Where $V_s$ is the charge voltage and $v_c(t)$ the voltage over the capacitor. If I want to derive this formula ...
2answers
2k views

### Opamp Inverting Amplifier: The case of non-inverting input not being connected to ground

What is the relation between $V_i$ and $V_o$ when the non-inverting input is supplied with a non-zero voltage level? I have shared my formula derivation below, but I can't validate it since I can'...
1answer
138 views

### Equation to calculate voltage divider resistor value for an input of op-amp

I found this guide for a temperature sensing circuit design with NTC thermistor by Texas Instruments. According to my opinion, optimum R1 value is calculated so that the voltage divider can provide ...
1answer
492 views

### How to interpret the equation $e=K_e.\omega_m$ in a BLDC context?

After researching a while on the subject, I noticed that several sources state that the back-emf constant of a BLDC motor satisfies the following equation: $$e = K_e.\omega_m$$ where: $e$ - ...
3answers
5k views

### independent control of frequency and duty cycle in 555 timer (formulas)

I want to control frequency and duty cycle of output pulse of 555 timer. I searched and find this schematic in a post in SOV but I don't know how calculate frequency and duty cycle in the circuit. ...
2answers
19k views

### When can I use the formula P=V^2/R?

I'm currently learning about the transportation of electrical energy through power lines. I now know that transporting current at a very high voltage cause minimal power loss compared to transporting ...
4answers
10k views

### How to Derive Capacitive- and Inductive Reactance Formula

I've been searching around the internet to find out how to derive the reactance formula for capacitors and inductors. But I couldn't really find anything, so I thought why not make a post about it. ...
2answers
455 views

### Is voltage divider formula stated wrong everywhere?

Sample voltage divider circuit: simulate this circuit – Schematic created using CircuitLab In this circuit, $Vout$ is, by Ohm's Law: $$Vin * \frac{R2}{R1+R2}$$ But this circuit, by itself ...
2answers
102 views

### Calculating for current in a single transistor amplifier(almost common collector?)

I was given this circuit for a practice test during one of my classes, but we were never shown how to actually solve it. It's just been bugging me so I wanted to know how others solved for all the ...
1answer
3k views

### Solar Power Watts/Volts/Amps

I have a 12v battery that is rated at 220ah. I have solar panels rated at 500 watts total. I'm using a MPPT charge controller rated for 12/24 volts I only have a rudimentary understanding of ...
1answer
50 views

### How to deal with controling force by positioning oscillating magnet?

I am trying to code up a closed loop control system on force generated by the paring of strong rare earth magnets. I do not have much experience with PID logic but i have a weak grasp of the basics (...
1answer
44 views

### Trying to find value of two capacitors using resonant frequencies in three conditions, but wrong formula is derived

I was trying to find capacitance of two capacitors in the following way. Connect each capacitor individually to a same inductor and find resonant frequency in each case. Connect the same capacitors ...
1answer
3k views

### Current draw calculations for a brush-less motor are way off

I've been attempting to calculate how much current a BLDC will draw given a known propeller size, thrust, internal resistance, Kv rating, Supply Voltage(Vin) and idle current. My propeller parameters ...
1answer
28 views

### How to properly calculate current of a variable capacitor?

So the formula i(t)=CdV/dt works for a constant value of a capacitor, but in a variable capacitor, i found the next formula on another site i(t)=C(t)*dV(t)/dt + V(t)*dC(t)/dt Is this formula ...
1answer
89 views

### How do I derive $(i_x)/(V_A-V_B)$ in this circuit?

I have this circuit below: http://qph.is.quoracdn.net/main-qimg-a5380479d6b436dcfb9a36252ac3f1c1?convert_to_webp=true Can I make the small signal equivalent circuit as shown below and when doing the ...
0answers
175 views

### Current derivative in RLC circuit

How to find the current derivative(di/dt) at t = 0+ in the first loop?
5answers
1k views

### What is the origin of the capacitance formula?

Everyone knows capacitance is defined as C = Q/V, but why? Sure I understand the utility of it and its use, but can someone provide a motivation or historical context for this definition? I'm unable ...
1answer
10k views

### I/O Resistance of common source MOSFET with source degeneration

Common Source MOSFET with source degenerations looks like this I am a bit confused about different input and output resistance statements (provided by different sources). Some of them say that ...
3answers
62k views

### Relationship of Induction Motor Frequencies

I would like to know how the mechanical rotor frequency [Hz] can be obtained from the electrical stator frequency [Hz]? This is no homework! I have consulted several books as well as the web but could ...
3answers
4k views

### Common Source JFET small signal equivalent circuit

This circuit is equivalent to small-signal common source JFET amplifier: If you look at the input and output impedance you can see that Zin = R1 || R2 and Zout = rd || Rd || Rl. It can be seen from ...
1answer
62 views

1answer
519 views

### How do I calculate, or measure, all values in a simple A.C. circuit?

I'm trying to figure out how all the formulae fit together regarding A.C. currents. Given this circuit and equations: I figured out the following: ...
1answer
60 views

### Deriving Wheatstone bridge equation

I have the following circuit: Here I have obtained the equation of Ud = U * ((deltaR / R)/(4+2(deltaR/R))). But I'm stuck on the part on how to derive that formula. Any help or guidance is ...
1answer
177 views

1answer
4k views

### Real output resistance of MOSFET

This question is related to MOSFET. NMOSFET's resistance was till now defined in many different ways, for example as: or which value varies from 1-50k Ohm. And there is also drain-source on-state ...